Identify the solution(s) of the system of equations, if any.
x + 2y = 6
3x - 6y = 0
A) (3, 2/3)
B) (3,3/2 )
C) (2/3, 3)
D) (3/2, 3)
3x + 6y = 18
3x -6y =0
6x = 18
x = 3
x +2y = 6
3 +2y =6
2y = 6
y = 3/2
Answer b
To find the solution(s) of the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
1. Start with the first equation: x + 2y = 6.
2. Solve this equation for x in terms of y:
x = 6 - 2y.
3. Substitute this expression for x in the second equation: 3(6-2y) - 6y = 0.
4. Simplify and solve for y:
18 - 6y - 6y = 0.
18 - 12y = 0.
-12y = -18.
y = -18/-12.
y = 3/2.
5. Substitute this value of y back into the first equation to find x:
x + 2(3/2) = 6.
x + 3 = 6.
x = 6 - 3.
x = 3.
Therefore, the solution to the system of equations is (x, y) = (3, 3/2), which corresponds to option D).